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Re: [Phys-L] just for fun



Open any math book and what do you see? Kids can do y = 4x, etc. Give them
F = ma and it's a whole new story. The way math has been taught is not
very useful for most people. Who really uses "algebra"? Who needs to?
What's the real value of a graphing calculator? Do the kids really
understand what they are doing?

Not the math teacher's fault. I wish math could be revolutionized to
include practical applications of what is being taught. What does a kid
learn in four years of high school math? How much of that is used in
science classes? And beyond high school, how much is used/needed in real
life?

These ideas recently (well, it's been ongoing) came up at our school, and
we plan to meet with the math department to share ideas, what kids
struggle with, when math topics are taught, etc. Science people are all
ready. Not sure the math people feel the same...


Phys-L@Phys-L.org writes:
I think it's important to teach the art of estimation. I agree with JD
that learning to solve problems as a general system is important,
powerful, and artful. Estimation another "coin of the realm" that every
(serious?) student should have. Don't be afraid to use convenient
fractional numbers, but get students to realize and remember such
numerical relationships that g_Earth~ pi^2 (SI units), sqrt(2), ln(2),
squares of integers from 1 to 20. Trinity, Little Boy, Fatman, and the
Nautilus were developed primarily with slide rules by people who were
trained to be numerate (is that a word, parallel to literate?)

That's why I favor ditching calculators until absolutely needed for
precise numerical work. I think calculators are being used to enable
"math" teachers who don't want the hard work of forcing students to work
hard. And calculators are being forced on the good math teachers who see
the destruction they are causing.

Do it, Anthony...teach at least one 6-8 week period without the
calculator. Yes, the students will whine. If the admin complains tell
them you will allow calculators when the football and basketball teams
quit running wind sprints and having 3-hour practices. (Easier for me to
say than for you to do.)

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Anthony
Lapinski
Sent: Thursday, December 19, 2013 9:36 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] just for fun

This is all very nice and interesting, but kids don't think like this.
They're not taught
to deal with fractions like this. Kids these days seem weaker than those
in the past.
They can't do basic fractions/decimals/estimations in their head (3/4,
2/5, 1/20, etc.).
They are literally lost without a calculator (or a cell phone). This is
the big downfall of
technology, which we are slowly seeing -- taking the thinking out of
learning. Much
easier to "click" than think.

Over the years I have thought about teaching physics without a calculator.
I could
essentially make up math problems where the numbers would come out as
simple,
non-repeating decimals. Might be difficult for the circular
motion/universal gravitation
topic, but I could always uses rounded numbers for the masses of the Sun,
Earth, etc.
And for projectile motion with trig, I could always use simple angles (30,
45, 60). The inverse
trig problems would be an issue. Maybe eliminate them? Still, kids would
have to do
basic algebra/fractions in their head. I've often wondered what the
results would
be like and how my students would handle this. I imagine not well at all,
so this is why
I have hesitated.

Anybody else thought about something like this?



Phys-L@Phys-L.org writes:

Surendranath

keep going
and now compare
1/6 with 1/8.5
and clearly 1/6 is bigger

faster for me

Richard




On Dec 19, 2013, at 9:56 AM, Surendranath <surendranath.b@gmail.com>
wrote:

how about 25/28 = (28-3)/28 = 1-3/28

and 15/17 = (17-2)/17 = 1-2/17

and compare 3/18 and 2/17


Best Wishes,

Surendranath

www.surendranath.org
www.youtube.com/user/Surendranath1954
https://play.google.com/store/search?q=pub:Surendranath.B.


On Thu, Dec 19, 2013 at 7:34 PM, John Denker <jsd@av8n.com> wrote:

The question was:

Which is bigger: 25/28 or 15/17? [1]

Here's my take: Write it as

a b
------- ¿>? ------- [2]
a + 3 b + 2

We know the value of a and b, so we don't need to solve
for them, but for now let's leave them as symbolic rather
than numeric.

Cross multiply. Throw away the "ab" term from both sides.
This leaves us with

2a ¿>? 3b

Now plug in the numeric values and do the multiplication.

I can do all of the above in my head, in less time than it
takes to find a pencil and paper.

=================

The larger point here is that sometimes it is /easier/ to do
the general case rather than the specific case. It's just
plain easier, even if only one specific case is of interest.
-- The advantage is even greater if there are multiple specific
cases on the agenda.
-- The advantage is even greater if the generalization provides
some insight into the structure of the problem, into the
nature of the problem.

There is artistry involved in finding a "good" generalization.
Equation [2] is not the only possible generalization of
equation [1].

The artistry is not however a shot in the dark. Experience
suggests patterns that are worth looking at. In this case
there is an analogy to differential-mode signaling. On the
LHS "a" is the common-mode signal, common to both numerator
and denominator, while "3" is the differential-mode signal.
Rewriting it so as to focus attention on what's common and
what's different is a technique that you can use in lots of
situations. There is no chance that HS students will have
the experience and expertise to do something like this, which
is why this is not a placement-test question but rather a
just-for-fun question.

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l

_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l



_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l